Unification of neural and wavelet networks and fuzzy systems

This paper analyzes several commonly used soft computing paradigms (neural and wavelet networks and fuzzy systems, Bayesian classifiers, fuzzy partitions, etc.) and tries to outline similarities and differences among each other. These are exploited to produce the weighted radial basis functions paradigm which may act as a neuro-fuzzy unification paradigm. Training rules (both supervised and unsupervised) are also unified by the proposed algorithm. Analyzing differences and similarities among existing paradigms helps to understand that many soft computing paradigms are very similar to each other and can be grouped in just two major classes. The many reasons to unify soft computing paradigms are also shown in the paper. A conversion method is presented to convert perceptrons, radial basis functions, wavelet networks, and fuzzy systems from each other.

[1]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[2]  Chuen-Tsai Sun,et al.  Functional equivalence between radial basis function networks and fuzzy inference systems , 1993, IEEE Trans. Neural Networks.

[3]  Leonardo Maria Reyneri,et al.  An Analysis on the Performance of Silicon Implementations of Backpropagation Algorithms for Artificial Neural Networks , 1991, IEEE Trans. Computers.

[4]  James J. Buckley,et al.  On the equivalence of neural nets and fuzzy expert systems , 1999 .

[5]  Roderick Murray-Smith,et al.  Extending the functional equivalence of radial basis function networks and fuzzy inference systems , 1996, IEEE Trans. Neural Networks.

[6]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[7]  Ignacio Requena,et al.  Are artificial neural networks black boxes? , 1997, IEEE Trans. Neural Networks.

[8]  Leonardo Maria Reyneri,et al.  Performance of weighted radial basis function classifiers , 1997, ESANN.

[9]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control , 1994 .

[10]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[11]  J. M. Ben,et al.  Are Arti cial Neural Networks Black Boxes ? , 1996 .

[12]  L. M. Reyneri.  Uni cation of Neural and Fuzzy Computing Paradigms , 1996 .

[13]  Leonardo Maria Reyneri,et al.  A comparison between weighted radial basis functions and wavelet networks , 1998, ESANN.

[14]  Bart Kosko,et al.  Fuzzy Systems as Universal Approximators , 1994, IEEE Trans. Computers.

[15]  Robert J. Hammell,et al.  Interpolation, Completion, and Learning Fuzzy Rules , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[16]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[17]  Qinghua Zhang,et al.  Using wavelet network in nonparametric estimation , 1997, IEEE Trans. Neural Networks.

[18]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[19]  Glenn Shafer,et al.  Readings in Uncertain Reasoning , 1990 .

[20]  M. Brown,et al.  On the functional equivalence of fuzzy inference systems and spline-based networks , 1995, Int. J. Neural Syst..